Conditional Distributions and Waiting Times in Multitype Branching Processes

Extinction times in Multitype Markov Branching Processes

In this paper, a distributional approximation to the time to extinction in a subcritical continuous-time Markov branching process is derived. A limit theorem for this distribution is established and the error in the approximation is quantified. The accuracy of the approximation is illustrated in an epidemiological example. Since Markov branching processes serve as approximations to nonlinear ep...

Limiting Distributions for Critical Multitype Branching Processes with Discrete Time(')

Relative frequencies in multitype branching processes

This paper considers the relative frequencies of distinct types of individuals in multitype branching processes. We prove that the frequencies are asymptotically multivariate normal when the initial number of ancestors is large and the time of observation is fixed. The result is valid for any branching process with a finite number of types; the only assumption required is that of independent in...

Random Laminations and Multitype Branching Processes

We consider multitype branching processes arising in the study of random laminations of the disk. We classify these processes according to their subcritical or supercritical behavior and provide Kolmogorov-type estimates in the critical case corresponding to the random recursive lamination process of [1]. The proofs use the infinite dimensional Perron-Frobenius theory and quasistationary distri...

Multitype Branching Processes in Random Environments

Consider a population of particles and k fixed particle classifications labeled type 1, type 2, ... , type k. Suppose that to each classification there corresponds exactly one k-variate p.g.f. and that each particle of the population is classified by one and only one type. Further, assume that after each unit of time, each particle, independently of the other particles, splits or disintegrates ...